Explicit Topological Priors for Deep-Learning Based Image Segmentation Using Persistent Homology

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35 Citations (Scopus)


We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from topological data analysis, to capture high-level topological characteristics of segmentation results in a way which is differentiable with respect to the pixelwise probability of being assigned to a given class. The topological prior knowledge consists of the sequence of desired Betti numbers of the segmentation. As a proof-of-concept we demonstrate our approach by applying it to the problem of left-ventricle segmentation of cardiac MR images of subjects from the UK Biobank dataset, where we show that it improves segmentation performance in terms of topological correctness without sacrificing pixelwise accuracy.
Original languageEnglish
Title of host publicationInformation Processing in Medical Imaging - 26th International Conference, IPMI 2019, Proceedings
EditorsSiqi Bao, Albert C.S. Chung, James C. Gee, Paul A. Yushkevich
Number of pages13
Publication statusPublished - 22 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11492 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Cardiac MRI
  • Persistent homology
  • Segmentation
  • Topological data analysis
  • Topology


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